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A priori and a posteriori error estimates for the Deep Ritz method applied to the Laplace and Stokes problem

Journal of Computational and Applied Mathematics, 2023
We analyze neural network solutions to partial differential equations obtained with Physics Informed Neural Networks. In particular, we apply tools of classical finite element error analysis to obtain conclusions about the error of the Deep Ritz method applied to the Laplace and the Stokes equations.
P. Minakowski, T. Richter
openaire +2 more sources

An iterative deep Ritz method for monotone elliptic problems

Journal of Computational Physics
In this work, we present a novel iterative deep Ritz method (IDRM) for solving a general class of elliptic problems. It is inspired by the iterative procedure for minimizing the loss during the training of the neural network, but at each step encodes the geometry of the underlying function space and incorporates a convex penalty to enhance the ...
Tianhao Hu, Bangti Jin, Fengru Wang
openaire +3 more sources

Food inflation pass‐through from agricultural imports in a small open economy

American Journal of Agricultural Economics, EarlyView.
Abstract This paper develops a new framework for quantifying cost pass‐through in a small open economy by estimating firm‐level markup responses to agricultural import price shocks. We show theoretically that markup adjustments depend on firms' reliance on imported inputs and demand curvature, generating heterogeneous inflationary effects across firm ...
Minseong Kang, Seungki Lee
wiley +1 more source

Managers' Sustainability Mindset: The Role of Place Attachment and Absorptive Capacity

Corporate Social Responsibility and Environmental Management, EarlyView.
ABSTRACT Sustainability mindset among managers is crucial for advancing sustainable development and creating long‐term environmental and social value. This study focuses on middle managers in Indian organizations and explores how place attachment and managerial absorptive capacity affect their sustainability mindset.
Asha K. S. Nair +2 more
wiley +1 more source

Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices [PDF]

, 2014
We propose a Preconditioned Locally Harmonic Residual (PLHR) method for computing several interior eigenpairs of a generalized Hermitian eigenvalue problem, without traditional spectral transformations, matrix factorizations, or inversions. PLHR is based
Knyazev, Andrew, Vecharynski, Eugene
core +1 more source

Grandmother's pregnancy complications and autism spectrum disorders in grandchildren, a California multigenerational cohort study

JCPP Advances, EarlyView.
Abstract Background Pregnancy complications have been associated with offspring autism spectrum disorders (ASD). There has also been increasing evidence for multigenerational risk factors of ASD. Methods In a multigenerational California birth cohort of 1,740,379 mother–child pairs, we investigated pregnancy complications when the grandmother was ...
Ting Chow +5 more
wiley +1 more source

Insight for Teacher Preparation Program Administrators: Enhancing Pre-service Educators\u27 lntercultural Sensitivity and Deep Proficiency in Culturally Responsive Teaching through Short-Term Study Abroad [PDF]

, 2018
Teacher preparation program administrators face the issue of expanding curricula to prepare teacher candidates for the diverse population of students they will encounter {Trent, Kea, Oh, 2008).
Boatman, Vikki +3 more
core +1 more source

On the functional window of the avian compass

, 2017
The functional window is an experimentally observed property of the avian compass that refers to its selectivity around the geomagnetic field strength.
Ganguly, Swaroop +3 more
core +1 more source

Genome‐Wide Assessment Reveals Ancestral Differences in Homozygosity Patterns Potentially Linked to Parkinson's Disease Etiology

Movement Disorders, EarlyView.
Abstract Background Recessive genetic variation and extended runs of homozygosity (ROHs) may contribute to the unexplained heritability of Parkinson's disease (PD), particularly in diverse and understudied populations. Objective We conducted the first large‐scale, multi‐ancestral investigation of PD to examine the impact of genome‐wide homozygosity on ...
Kathryn Step +680 more
wiley +1 more source

Superconductivity in the Two-Dimensional $t$-$J$ Model at Low Hole Doping

, 1994
By combining a generalized Lanczos scheme with the variational Monte Carlo method we can optimize the short- and long-range properties of the groundstate separately.
Ceperley D M +9 more
core +2 more sources

numerical analysis math.na
fos: mathematics
mathematics - numerical analysis

fos: computer and information sciences
artificial neural networks and deep learning
machine learning cs.lg

neural networks
computer science - machine learning
partial differential equations